How to calculate the Probability of Deficiency of the AQL of an Inspection

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David-D

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#12
One thing that is actually useful is comparing the two sets of results to see if they are actually statistically significant. As mentioned above, AQLs are a long-term game of overall, given that quality level you will accept it ~95% of the time but each individual sampling is a gamble based on the OC curve for the sampling plan.

I like comparing the results of two different samples with a Fisher exact contingency test. This helps you judge of the difference is just random luck or if it is more likely to be an actual difference (non-homegeniety, test method differences, sampling issues, etc).

David
 

Statistical Steven

Statistician
Staff member
Super Moderator
#13
David, I caution you on that approach.

Unless the two sets of results have similar sample sizes. The Fisher's exact (or any binomial comparison of proportions) is sample size dependent. Here is an example to illustrate my point

10/100 =10%
50/1000 = 5%
Fisher's p-value is 0.059

5/100 = 5%
100/1000 = 10%
Fisher's p-value is 0.150

5/100 = 5%
10/100 = 10%
Fisher's p-value is 0.283

50/1000 = 5%
100/1000 = 10%
Fisher's p-value is 0.000

So comparing a set with 5% to one with 10% defective can give different levels of statistical significance based on sample size.






One thing that is actually useful is comparing the two sets of results to see if they are actually statistically significant. As mentioned above, AQLs are a long-term game of overall, given that quality level you will accept it ~95% of the time but each individual sampling is a gamble based on the OC curve for the sampling plan.

I like comparing the results of two different samples with a Fisher exact contingency test. This helps you judge of the difference is just random luck or if it is more likely to be an actual difference (non-homegeniety, test method differences, sampling issues, etc).

David
 
L

leturc

#14
Dear All,

Thanks a lot for your reply but I'm little bit lost.

We're often using Lev II for sampling and 0,065% for Critical defects, 2,5% for Major defects and 4,0% for Minor defects.

We made an inspection with following results:
Lot size: 3600 pieces
Sampling size: 200 pieces
Defects found
Critical: 0 agains 0 tolerated
Major: 12 against 10 tolerated
Minor: 14 against 14 tolerated

As a result the lot failed.

But, still with the same conditions the 2nd sampling done just after the 1st one give a better result.

Lot size: 3600 pieces
Sampling size: 200 pieces
Defects found
Critical: 0 agains 0 tolerated
Major: 4 against 10 tolerated
Minor: 12 against 14 tolerated

I'm aware that this is the risk of random sampling (accept bad lots / refuse good lots).

And it is very difficult to make understand this to our client. They don't want to understand this and I need to give them a better explanation.

Is there any calculation that can give to me the possible deviation?

How can I draw OC curves for above examples?

Thanks again for your help this helped me to understand better the concept.
 

Statistical Steven

Statistician
Staff member
Super Moderator
#15
Let's start at the beginning. OC curves are for the sampling PLAN not the sample you take. Let's use the critical level defects for example. You claim with a sample size of 200, acc/rej=0 that equates to an AQL of 0.065%. The AQL means that on AVERAGE a lot with 0.065% defective will pass the sampling plan 95% of the time. This means that on average 95 out of 100 samples of 200 units from a LOT with 0.065% defective will have 0 defects. It also means that 5% of the time, even though the lot has 0.065% defective, you will find at least 1 defective in your sample.

So when you inspected the lot initially, it failed. The second sample passed. Some might say that your first sample was a Type I error (1 of the 5 that should have passed). Others might conclude your second sample was a Type II error (it's a bad lot, but you got a passing sample). Unless you do 100% sampling, you never know for sure which error it.

Does that help?



Dear All,

Thanks a lot for your reply but I'm little bit lost.

We're often using Lev II for sampling and 0,065% for Critical defects, 2,5% for Major defects and 4,0% for Minor defects.

We made an inspection with following results:
Lot size: 3600 pieces
Sampling size: 200 pieces
Defects found
Critical: 0 agains 0 tolerated
Major: 12 against 10 tolerated
Minor: 14 against 14 tolerated

As a result the lot failed.

But, still with the same conditions the 2nd sampling done just after the 1st one give a better result.

Lot size: 3600 pieces
Sampling size: 200 pieces
Defects found
Critical: 0 agains 0 tolerated
Major: 4 against 10 tolerated
Minor: 12 against 14 tolerated

I'm aware that this is the risk of random sampling (accept bad lots / refuse good lots).

And it is very difficult to make understand this to our client. They don't want to understand this and I need to give them a better explanation.

Is there any calculation that can give to me the possible deviation?

How can I draw OC curves for above examples?

Thanks again for your help this helped me to understand better the concept.
 

Mike S.

Happy to be Alive
Trusted Information Resource
#16
And it is very difficult to make understand this to our client. They don't want to understand this and I need to give them a better explanation.

Is there any calculation that can give to me the possible deviation?
Well, if "they don't want to understand this" no amount of explanation on your part will help. Are they trying to "shoot the messenger"?

The results of the 2 samples you took look quite possible to me...they pass the "sniff text" as reasonably possible.

Is there reason to believe your lot of 3600 is homogeneous?
 

howste

Thaumaturge
Super Moderator
#17
That's why it's called "probability" and statistical inference. Sampling always has uncertainty involved. Statistically speaking, the first sample results said the lot is "probably" not acceptable. The next logical step would be to either reject the whole lot or do 100% inspection.

I'm curious why a second sample was taken. The fact that you're using a sampling plan which accepts known defects (and not a C=0 plan) indicates that the process/customer must be able to tolerate some nonconformities.

Customers who don't understand statistics are always going to complain anytime they get nonconformities even though the sampling plan they accepted has a probability of passing some through at some time. If you want the customer to understand why you're using a sampling process, just give them a quote for what it will cost them for you to do 100% inspection instead.
 
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